Tutorial eBooks PDF File Download

This paper describes Newton and quasi-Newton optimization algorithms for dynamics-based robot movementgeneration. The robots that we consider are modeled as rigidmultibody systems containing multiple closed loops, active andpassive joints, and redundant actuators and sensors. While onecan, in principle, always derive in analytic form the equations ofmotion for such systems, the ensuing complexity, both numericand symbolic, of the equations makes classical optimization-basedmovement-generation schemes impractical for all but the simplestof systems. In particular, numerically approximating the gradientand Hessian often leads to ill-conditioning and poor convergencebehavior. We show in this paper that, by extending (to the generalclass of systems described above) a Lie theoretic formulation ofthe equations of motion originally developed for serial chains,it is possible to recursively evaluate the dynamic equations, theanalytic gradient, and even the Hessian for a number of physicallyplausible objective functions. We show through several case studiesthat, with exact gradient and Hessian information, descent-basedoptimization methods can be forged into an effective and reliabletool for generating physically natural robot movements.